On the Fukaya-Morse A-infinity category

Apparaît dans la collection : 2023 - T2 - WS1 - GAP XVIII: Homotopy algebras and higher structures

I will explain the construction of the Fukaya-Morse category of a Riemannian manifold X -- an A-infinity category where the higher composition maps are given in terms of numbers of embedded trees in X, with edges following the gradient trajectories of certain Morse functions. I will give simple examples and explain different approaches to understanding the structure and proving the quadratic relations on the structure maps -- (1) via homotopy transfer, (2) effective field theory (“second quantization”) approach, (3) topological quantum mechanics (“first quantization”) approach. The talk is based on a joint work with O. Chekeres, A. Losev and D. Youmans, arXiv:2112.12756.

Informations sur la vidéo

Date de captation 25/05/2023
Date de publication 25/05/2023
Institut IHP
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Alexandre Duplessis
Format MP4
Lieu Amphitheater Hermite, IHP

Domaine(s)

Physique mathématique

Bibliographie

Olga Chekeres, Andrey Losev, Pavel Mnev, Donald R. Youmans : Two field-theoretic viewpoints on the Fukaya-Morse A-infinity category / arXiv:2112.12756